The land-use pattern for many cities is a central business district surrounded by sprawling suburbs. This pattern can lead to an inefficient and congestion-prone transportation system due to a reliance on automobiles, because high-capacity transit is not efficient in low-density areas where insufficient travelers can access transit. This also poses an equity concern as the monetary cost of faster and more expensive travel disproportionately burdens low income travelers. This dissertation presents a deterministic approximation of a discrete choice model for mixed access and mainline transportation modes, meaning that travelers may use different modes to access a mainline system, such as transit. The purpose is to provide a tractable computationally efficient model to address the first/last mile problem using a system-wide pricing policy that can account for heterogeneous values of time; a problem that is difficult to solve efficiently using a stochastic model. The model is structured for a catchment area around a central access point for a mainline mode, approximating choice by comparing modal utility costs. The underlying utility model accommodates both fixed prices (e.g., parking, fixed tolls, and fares) and distance-based unit prices (e.g. taxi fare, bike-share, and distance tolls) that may be set in a coordinated way with respect to value of time. Using numerical analysis, the deterministic model achieved results within 4% accuracy of a stochastic logit-based model, and within 6\% of measured values. The final model achieved a 57% reduction in generalized travel time and improved the Gini inequity measure from 0.21 to 0.03.